If this were true, there wouldn’t be need for the Mexico City Policy. The Hyde amendment only applies to omnibus spending bills to which it is attached. For example the
2009 Omnibus. A FAQ on the Hyde amendment is
here). From the Hyde amendment:SEC. 507. (a) None of the funds appropriated in this Act, and none of the funds in any trust fund to which funds are appropriated in this Act, shall be expended for any abortion.
Now, funds allocated in other acts are not subject to the Hyde amendment (such as Obamacare). Indeed, the primary target of the Mexico City policy was USAID, which was not funded by the omnibus spending bills, and was thus not affected by the Hyde amendment.
Only insofar as they provide abortion services. Poor countries have the choice of offering health services that don’t include abortion and receive federal aid, or they can choose to go without and offer abortion services. Don’t blame the Mexico City policy for poor countries’ lack of funding for health services.